यदि `cosec A =sqrt2` तो, `(2 sin ^(2)A+3 cot^(2)A)/(4 tan ^(2) A-cos ^(2) A)` का मान ज्ञात करो।

Explanation

दिया है:
`cosec A =sqrt2 implies(1)/(sin A ) =sqrt2 impliessin A =(1)/(sqrt2)`
`therefore cos A =sqrt(1-sin ^(2)A)impliescos A =sqrt(1-((1)/(sqrt2))^(2))=(1)/(sqrt2)`
`tan A =(sin A)/(cos A)impliestan A =((1)/(sqrt2))/((1)/(sqrt2))=1` तथा `cot A=(1)/(tan A )implies cot A =1/1 =1`
`therefore(2 sin ^(2) A+3 cot ^(2)A)/(4 tan ^(2)A-cos ^(2)A)=(2xx((1)/(sqrt2))^(2)+3(1)^(2))/(4(1)^(2)-((1)/(sqrt2))^(2))=(2xx(1)/(2)+3)/(4-(1)/(2))=(1+3)/(7//2)=8/7`